WAY MAWSTON

if,:l J r < l k l A R YAI'I~I.I(~,YI'IOX

'1.1 r:or< I<I.:~- peda~lccwoulcl be 10 ohms, allclonatil irlcI~lc~ri\/c cap;~citive(LC) the entire signal voltage wouldfilters these days arc in high- l ~ gc~ieratrd r across k.f'rcque~~c). c:ircuits. 'l'licse f i l - Tiic signal currents throughLers. like resis:i\le capacsirive INPUT e f f c c ~ i \ / cr e s i s t a ~ ~ c .Re flow(I<Cl filters cxn easil!. be dc- through (' and I., whirh bothsigned to perform low-pass. have I-eac:tanc.cs 100 t i m e shigh-pass, bandpass, or north greater than tlie val11e of K illfiltcrinq, b ~ l the!. t have [he addi- n l ~ m s Coiisec~~~cn~ljr. . the signaltional l;e~ic.fi~ ol'oi'fcriiig at lcasl ;f b12 dB pcr oc:tav: of rolloff. (,om- -4 7 - - . - -. . . -pared LO the 6 dE3 per octa\~eof FIG. 1-LC SERIES-RESONANT filters: fRC lilters, cl.llic,h sharDer simplified . .. . schematic, a, and equivalent 'I Icutoff characteristics at all oier- Iating frequencies. OHMS The series- and the parallel- At some specific frequency,resonant LC filters are the two the reactances of C and L could"watershed" LC designs from be 10 kilohms and I kilohm, re-which all others are derived. spectively Therefore the filtersFigure I - a shows a circuit for a input impedance (ignoring theseries-resonant filter, and Fig. value of R ) will be 9 kilohms at1-b shows its simplified equiv- that frequency. Many other sim:alent circuit. The R represents ilar examples can be given.the resistance of the coil. The key point to be made here is that at resonant frequency,J,,Series-resonant filter the reactances of C and L will be The fundamental response of equal (but 90" out of phase),the series filter is that capacitive and the filter input impedancereactance C decreases with in- will equal the value of R, as indi-creased frequency, while induc-tive reactance decreases. The cated by the dotted line at the bottom of the impedance vs. fre- FREQUENCY---, - a b 2.inverse relationship also holds. quency characteristic curve Fig. 0 in FIG. 2-LC SERIES-RESONANT FILTER: zThe filler's input impedance is 2-a. For example, if this occursequal to the difference between when the reactances of C and L Plot of input impedance vs. frequency at resonance, a, plot of voltage output vs. 2these two reactances, pius the are both 1000 o h m s , a n d R frequency at resonance taken across Lvalue of resistor R. equals 10 ohms, the input im- or C, Is. 69voltage generated across C and Notice in Fig. 2-b that the in-L is 100 times greater than the ductive and capacitive voltagesactual input signal voltage, as are 90" out of phase, and theshown in Fig. 2-b, the curve of voltage generated across the se-voltage vs. frequency. This volt- ries LC combination is effec-age magnification, indicated by tively zero. The impedence ofthe sharp peak, is known as the the filter at f, is known as thecircuit's Q. filter's characteristic imped- ance, Z,, and it equals a. Figure 3 shows two ways to make practical use of a series- resonant LC filter: In Fig. 3-a, 2.2 kilohm resistor R, and the filter act together a s a frequen- cy-selective a t t e n u a t o r t h a t gives high attenuation at the r e s o n a n t frequency f,, a n d lower attenuation above or be- low that resonant frequency. (The filter is a notch rejector.) In Fig. 3-b, the input signal is applied directly to the filter, and the output is taken across the inductor L. This filter circuit acts a s a notch acceptor that provides high gain at resonantnotch rejector, a, and notch acceptor, b. frequencyf,and low gain above or below that frequency. I

Table 1 lists the principal for-

rnulas that can be applied to both series- and parallel-reso- nant LC circuits. Parallel-resonant filters Figure 4-a shows the sche- matic for a parallel-resonant fil- ter, a n d Fig. 4-b shows i t s equivalent circuit. The induc- tor's resistance is represented by R. In this filter, capacitive re- actance decreases with increas- ing frequency,and inductive reactance increases with in- creasing frequency. The re- ciprocal relationship also holds. Each component draws a sig- nal current that is prop?rtional to its reactance, but the two cur- rents are 90" out-of-phase, s o FIG. 5-LC TUNED AMPLlFlERS withters: simple schematic, a, equivalent cir- low-impedance outputs: transformercuit, b, and plot of input impedance vs. the total signal current is equal coupiing, a, auto-transformer coupling,frequency, c. to the difference between the L b, and capacitive-divider coupling, c.

and C currents. At resonance, L

and C are equal so the total cur- rent falls nearly to zero. As a result, the filter acts as a near-infinite impedance. In practical filters,the presence of equivalent resistance R modi- fies the response by reducing 'the impedance at the resonant frequency f,, Z,, to Zo2/R. For example, if Zo equals 1 kilohm and R equals 10 ohms, the value of Z , will be 100 kilohms. come this drawback are illus- LC oscillators trated in Fig. 5. Figures 6 through 10 illus- One way to obtairi output trate the different schemes for coupling is to consider the pri- using a parallel-resonant filter mary winding of an RF trans- as the tuning element in tran- former as the filter's inductive sistorized LC oscillators. The component, and to take the out- simplest of the LC oscillators is put from the transformer's sec- the tuned-collector feedback ondary, as shown in Fig. 5-a. form shown in Fig. 6. This approach provides a fully Transistor Q1 is connected a s floating output. If the trans- a common-emitter amplifier, L1 former has a 10:l turns ratio, and C1 form the tuned collector the output signal will have an filter, and L2 provides the collec- attenuation factor a of 10. tor-to-base feedback. Inductor In a second method, the coil L2 is inductively coupled to L1,FIG. GTUNED-COLLECTOR feedback can be tapped as shown in Fig. providing transformer action.LC oscillator. 5-b, to obtain an output by au- By adjusting the phase of this totransformer action. In the feedback signal, the circuit will third method, as shown in Fig. give zero phase shift at the 5-c, the required tuning capaci- tuned frequency so that, if the loop gain (determined by Tl's turns ratio) is greater than uni- ty, the circuit oscillates. With the component values shown, oscillation frequency can be var- ied from 1 MHz to 2 MHz by trimmer capacitor C1. Figure 7 is the schematic for a simple Hartley oscillator. The turns of collector load inductor L1 are tapped at a point 20% down from the top of the coil, and the circuit's positive power supply is connected to this tapFIG. 7-SIMPLE HARTLEY LC oscillator. FIG. &COLPITTS LC OSCILLATOR pro- point. As a result, L1 acts as an duces a 37-kHz output. autotransformer so that the sig- Figure 4-c is the filter's fre- nal voltage appearing at the top quency response: a plot of input of L1 is 180" out of phase with impedance vs. frequency show- the voltage at its low end (near- ing how the input impedance est Ql's collector.) peaks at the resonant frequency The signal voltage at the top off,. All of the formulas in Table 1 the coil, (which is 180" out of apply to the parallel-resonant phase with the signal at Ql's col- filter as well. lector) is coupled the base of Q1 base by isolating capacitor C2.Output coupling In this arrangement the circuit The two most popular ap- oscillates at a center frequencyplications for parallel-resonanttuned filters are in narrow fre-quency band amplifiers and inLC oscillators. In narrow-band FIG. 9-CLAPP OR GOURlET LC 0s-amplifiers t h e filter usually cillator producese an 80-kHz output.functions as the collector loadfor common-emitter amplifiers tance is obtained from two se-a s shown by three simplified ries-connected capacitors. Anschematics in Fig. 5. The filter output can be obtained acrossprovides high gain at its reso- the larger capacitor by capaci-nant frequency and lower gain tive divider action.above and below that frequency. In these schematics each cir- The drawback to these cir- cuit has arbitrarily been givencuits is the problem of gaining a n attenuation factor a of 10.access to the circuit's output Each has an output impedances i g n a l s w i t h o u t loading t h e of Z,/a2. Thus, if Z, equals 100tuned circuit and lowering its kilohms and a equals 10, the Zeffective Q . Three ways to over- output equals 1 kilohm. cillator. Gouriet oscillator offers excel- lent frequency stability. With the component values shown in the schematic, it will oscillate at about 80 kHz. Figure 10 is a schematic for a Reinartz oscillator. Its tuning coil has three inductively cou- pled windings. Positive feed- back is obtained by coupling the collector and emitter signals of the transistor through coils L1 and L2. Both windings are inductively coupled to L3. The Reinartz oscillator oscillates at a frequency determined by the values of L3 and C1. The coil- turns ratios are typical for a cir- cuit designed to oscillate at a few thousand kHz. FIG. 13-L-TYPE HIGH-PASS FILTER: FIG. 11-FALSE L-TYPE LOW-PASS fil- schematic, a, and frequency response ter: schematic a, and frequency re- curve. b. sponse curve.

determined by the values of L

and C. In general, circuit oscillation depends on tapping a common signal at a point in the tuned circuit so that phase-splitting autotransformer response is obtained. This tap point need not be made in the tuning coil; it can be made in the tuning capacitor, as in the Colpitts os- cillator shown in schematic Fig. 9. With the component values in that figure, the oscillator will os- cillate at about 37 kHz. In Fig. 8, C1 is in parallel with FIG. 14-LOW-PASS LC FILTERS: T-sec- transistor Ql's output capaci- tion schematic, a, and %-section,b. tance, and C2 is in parallel with FIG. 12-TRUE L-TYPE LBW-PASS filter: Ql's i n p u t capacitance. Con- schematic, a, and frequency response sequently, capacitance changes curve, b. caused by ambient and compo- nent temperature changes can Low-pass and high-pass shift the oscillation frequency. Figure Il-a is a schematic for This shift can be minimized a "false" L-type low-pass filter. and good frequency stability Inductor L and capacitor C act can be obtained by selecting val- together as a frequency-depen- ues for C1 and C2 that are large dent attenuator. At low frequen- with respect to Ql's internal ca- cies the reactance of L is low and pacitance. the reactance of C is high, so the Figure 9 shows a modifified circuit offers negligible attenua-3 version of the Colpitts oscillator, tion. At high frequencies the're-8 known as the Clapp or Gouriet actance of L is high and that of$ oscillator. Another capacitor, C is low, so the circuit offers FIG. 15-HIGH-PASS LC FILTERS: T-sec- C3, with a value that is small high attenuation. tion schematic, a, and %-section,b. relative to C1 and C2, is put in Consequently, the circuit acts series with L1. This circuit's res- like a low-pass filter. It is called it circuit is actually a series-reso- onant frequency is determined a "false" filter because the cir- nant filter (like Fig. 1) with its2 output taken from across ca-5 principally by the values of L1 cuit will only function correctly and C3 and it is almost inde- if it is driven from a source im- pacitor C. pendent of variations in tran- pedance equal to 2,. (This is If the circuit is driven from a72 sistor capacitance. The Clappl not shown in the diagram.) The continued on page 89duce a required sound-pressure all play a part in squeezing the max- but informative, power-handling ca-level from a given loudspeaker, it imum power rating from any .given pability specification, such as thatclips the positive and/or negative speaker. used by Allison Acoustics: ' a t leastpeaks of the musical waveforms. The test signal used to derive a 15 watts continuous at any frequen-Short-duration overloads may not system's power rating must be cy. Over most of the frequencybe audible; longer overloads are fre- chosen carefully. The ubiquitous range, at least 350 watts for 0.1quently perceived as level compres- pink-noise signal used in so many second, 125 watts for 1 second, 60sion, rather than distortion. How- other audio tests is totally inap- watts for 10 seconds."ever, badly overdriven amplifiers propriate for power testing be- N o t e the distinctions Allisonproduce a raspy distortion, not un- cause, unlike music, it has equal makes between continuous andlike that of a mistracking phono car- energy per octave. In contrast with transient wattage levels. The dif-tridge. Low bass passages are likely the midrange energy hump dis- ference between them is what al-to take on a "mushy" quality be- played by most music, pink noise lows you to play very loud musiccause of the spurious harmonics shows up on a real-time analyzer as without problems, even though agenerated by the overload. And as a virtually straight line, which is a continuous sinewave at the samediscussed earlier, prolonged opera- poor representation of music. peak level would certainly damagetion with hard clipping is a frequent The single rms ratings used by your audio equipment. In othercause of driver damage, so clipping some manufacturers imply the use words, your 100-watt (or even 200-should be avoided. of a sinewave test signal, which, watt) amplifier is certainly safe to again, is totally unlike a musical use with typical speakers rated atProper power ratings waveform in shape or energy con- 50 watts maximum so long as you Arriving at a speaker system's tent. The most valld and informative don't feed continuous tones or pinkpower rating is no easy task, even way for a manufacturer to specify a noise to them, drive the amplifierfor its designer. Ideally, a manufac- speaker's power-handling capability into hard clipping, drop a tone arm,turer designs for the highest power is to state, however loosely, the or lose a cable ground at high vol-capability that can be achleved with- power it can handle in a specific ume. In short, you have to abusein his cost and size constraints for a frequency range for a specific your speakers (and your ears) be-given model. Special high-tempera- amount of time. fore disaster is likely to strike. If youture materials such as voice-coil Listing specifications that way don't ask for trouble, it probablywire, voice-coil forms, and cements gives rise to a somewhat complex, won't happen. (I

puts loaded by, a specific imped-

ance value. S u c h filters can readily be cascaded to yield very high levels of signal rejection.low-impedance source, the out- Among those filters are the T-put will produce a steep signal section and pi-section low-passpeak a t f,,as shown in the fre- filters that are shown in Fig. 14,quency-response curve of Fig. and the T-section and pi-section11-b. The magnitude of this high-pass filters that are shownpeak is proportional to the cir- in Fig. 15.cuit's Q. All of these filters exhibit a n Figure 12-a shows how Fig. output rolloff of about 12 dB per11-a can be modified so that it filter reiects interference on the power octave (40dB per decade). Their-behaves like a true L-type low- line to about 25 MHz. outputs must be correctly load-pass filter. Resistor Rx is placed ed by a matching filter sectionin series with the circuit's input rather than across capacitor C, or terminating load. The designso that the s u m of R, and R, The value of equivalent resistor formulas for them are given in(the input signal's source im- Ex in both of these circuits can Table 1.pedance) and R (the equivalent be reduced to zero if the filters Figure 16 shows an applica-resistance of L) equals the cir- 2, value is selected to match R,, tion for a T-section low-pass fil- 2cuits characteristic impedance as given in formula 2 of Table 1. ter-an AC power-line filter that +2,. The addition of this resis- The outputs of these filters, like will block interference that is on 2tance reduces the circuit's Q tounity, but it results in a clean those of the series and parallel- resonant filters, must "see" only the line from reaching a sen- sitive unit of equipment while " -C3

low-pass filter output shape as high-impedance loads to oper- also blocking any interference $shown in Fig. 12-b. ate properly from that might be generated 2. Figure 13 illustrates how the The most popular low-pass internally by t h a t u n i t fromprinciple just discussed can beapplied to make a n efficient L- and high-pass filters are bal- anced, with matched imped- reaching the power lines. This circuit can be made t o operate ftype high-pass filter. The output ances that are designed to be at frequencies up to about 25i s t a k e n across i n d u c t o r L driven from, and have their out- MHz. 12 89